3. Stone-Geary felicity) Consider the following utility maximization of some consumer over time. cr(e(t)-c)사-l eMt subject...
6.Consider the following utility maximization of some consumer over time. Max "dt subject to a(0)a(T)-0 a(t)-w(t)x1+r(t)xa(t)-ct) where w(t) and r(t) are given paths of real wages and the real rate of return of the single asset and σ # 1 is a positive constant. The parameter c represents the minimum a(t)- w(t)x1+r(t)xa(t)-c(t), subsistence level of consumption. Compute the Euler equation.
2. (CES felicity) Consider the following utility maximization of some consumer over time. /or(e(t)/σ e-ptdt subject to k(0)-k(T)-0, Max a (r) =n(t)x 1+r (t) x a(t)-c(t). where w(t) and r(t) are given paths of real wages and the real rate of return of the single asset and σ 1 is a positive constant. Compute the Euler equation.
1. (logarithmic felicity) Consider the following utility maximization of some consumer over time. Mr,( .1。[loge(t) e--dt subject to k(0)=k(T)=0, a(t)-w(t)x1+r(t)xa(t)-c(t). where w(t) and r(t) are given paths of real wages and the real rate of return of the single asset. Compute the Euler equation.